Review of book "Majority Judgment"

[Warren Smith]

From: Steven J. Brams
Date: Mon, Aug 22, 2011 at 10:15 AM
Subject: Review of Majority Judgment

I thought my review of Majority Judgment in the Sept.-Oct. issue of
American Scientist would be of interest to you and your
election-science colleagues:

http://www.americanscientist.org/bookshelf/pub/grading-candidates

Best wishes,
Steven J. Brams                     Phone: (212) 998-8510
Dept. of Politics                   FAX: (212) 995-4184
19 West 4th St., 2nd Floor          E-mail: steven...@nyu.edu
New York University
New York, NY  10012

[Jameson Quinn]

Doesn't seem much like a review; more like a coat-hanger for Brams's own views. And not a very convincing one... any voting analysis which focuses on the pathologies of a system you don't like, without considering either how frequently those would arise or any corresponding pathologies of your favored system, isn't to be trusted. (Especially since at least one of the "pathologies" Brams mentions is that MJ could have elected a non-centrist in France, something B+L tout as a positive benefit.)

JQ

2011/8/22 Warren Smith <warre...@gmail.com>

[Warren Smith]

> Brams:

> I thought my review of Majority Judgment in the Sept.-Oct. issue of American
> Scientist would be of interest to you and your election-science colleagues:
>
> http://www.americanscientist.org/bookshelf/pub/grading-candidates

--I have a quibble with one point, or speculation, that Brams makes in
his book review.
I'll get to it in a little while. First I want to point out this page
http://www.rangevoting.org/French2007studies.html
which discusses the France 2007 election and the several simultaneous
studies (Balinski
& Laraki's among them) that were conducted with different voting
systems using real
French voters.

Sarkozy won both officially and in the Instant Runoff study.
Bayrou won in the Balinski/Laraki "majority judgmt" study, as well as
in the independent approval voting and range voting study, and was a
Condorcet winner based both on pairwise-poll data and the rank-order
ballot study
data.

Also using these studies' data but other voting methods applied to that data
we can try to see (and I did) what other voting methods would have done.
All the methods I considered elected Bayrou except for IRV & plurality
which elected Sarkozy.

The IRV election appears to have been non-monotonic (again...) as I
explain in that
web page; but for 100% certain confirmation I would need to see their
raw vote data,
but the IRV-study authors Etienne Farvaque, Hubert Jayet, Lionel Ragot
ignored my request for it.

MY QUIBBLE WITH BRAMS:
One thing I noticed in the Brams book review that
I looked into further -- finding in the end it looks like Brams
guessed wrong --
was Brams noting that B&L had noted that maybe with Majority-Judgmt Bayrou
would NOT have won... then Brams continued on to imply that this was a DEFECT
both in Majority-Judgmt and in Range Voting [maybe both would not have
elected Bayrou]
as opposed to: Approval would have correctly elected Bayrou.

Bayrou did win using the Majority-Judgmt votes Balinski+Laraki
collected in Orsay,
but since Orsay was a pro-Bayrou region of France (Bayrou won
officially in Orsay)
that does not necessarily mean Bayrou would have won using MajJudgmt
if conducted in all France.

So let me look a little deeper into this claim/speculation by Brams.

1. Bayrou won using Balinski&Laraki's Orsay votes using either median,
or 2 kinds of average, but that does not necessarily mean Bayrou would
have won in all France. But for what it is worth, Bayrou's average
was 3.13 and 3.04
computed 2 ways, while the median was 3.00; this contrasts with
Royal 2.82, 2.77, 3.00 and Sarkozy 2.52, 2.48, 3.00. My point is
average-based range at
least naively had a greater margin for Bayrou than median-based range (which
was a 3-way tie broken using B&L tiebreak procedure).
If the top 3 Majority-Judgmt scores were regarded as "approve"
and the bottom 3 as "disapprove" (this is a crude guess & cannot be
taken too seriously)
then Bayrou 69.4% approval, Royal 58.5, Sarkozy 53.2, others<=30.3 each.
This at least naively is a greater Bayrou margin with guessed-Approval than
with range, almost twice the margin. Also a less-naive view of MajJudgmt
(now explicitly considering the tiebreak data as part of the "margin")
would indicate that actually the MjJudgmt "real margin" was exactly the
same as this guessed-approval margin since the approvers were for
these 3 candidates
exactly the voters coring at or above median.

2. Bayrou also won using the Baujard-Igersheim approval-voting and
range-voting data sets.
These have to be taken more seriously since they are genuine data, not
a crude guess.
Their approval results Bayrou 42.8%, Royal 41.6, Sarkozy 35.9
were a 3X smaller margin than the average-based-range margin using
B&L's vote data. More importantly it also was a 4X smaller margin than the
Bayrou=1.08, Sarkozy=0.96, Royal=0.94 range voting {2,1,0 scores}
data collected by Baujard+Igersheim from the SAME voters as their
approval voters.

3. What about the "all of France" versus "where we collected the data"
discrepancy this time for Baujard+Igersheim rather than Balinski? If
you look in Baujard+Igersheim's immensely long 279-page report, section 3,
Tableau 26 thru 31 give the official results in their 6 locations finding
n three Bayrou was officially way in third place, and in the other three way
in second place and close to third (combining official results puts
Bayrou in third,
see Tableau 33 & 34), even though Bayrou won these locations using approval
and with range voting! This suggests that Bayrou WOULD HAVE WON with approval
voting in all of France, and also would have WON BIGGER with range voting in
all of France. Baujard & Igersheim agree with me;
they did an "extrapolation to all of France" by 3 different methods and
all three extrapolations concluded (Tableau 36) that Bayrou would have won
with approval (note they call "range voting" by the name "vote par
note," as opposed to
"vote par approbation") and comparing their tableau 108 & 109
they also agree with me the Bayrou-wins margin would have been bigger
using range voting
(approximately a factor 1.40 bigger in their 6 locations combined).

4. Balinski & Laraki apparently never attempted a careful
extrapolation to all of
France, unlike Baujard+Igersheim, so things are less clear with
{0,1,2,3,4,5} range
voting. (But maybe they did do such an extrap. in their book, which I
have not seen?)

BOTTOM LINE:
So contrary to Brams' intuition about range vs approval, Bayrou would
have won France with approval and would have won bigger with
average-based {0,1,2} range voting.

With {0,1,2,3,4,5} average-based range voting, I'm less confident.
Nevetheless overall I think Bayrou's victory was more likely
with {0,1,2,3,4,5}range than with approval voting.

(This all might be another though minor example of "nursery effect."
In that effect, range voting tends to help third-party candiates,
especially from
weak third parties, more than approval voting helps them. Bayrou's third party
was a pretty strong one so we would expect the
nursery effect to be weak, but anyhow this elections seems to confirm it.)

[Warren D. Smith (CRV cofounder, http://RangeVoting.org)]

Brams says I misunderstood what he was saying -- says he agrees with
me Bayrou would
have won in France 2007 with Range and Approval, but thinks Bayrou
plausibly still would have lost with MajJudgmt.